59 citations · 162 across the 30 of their papers we have counts for
30 papers
Asymptotics of Riemannian Lie groups with nilpotency step 2
Enrico Le Donne, Luca Nalon, Sebastiano Nicolussi Golo +1
We derive sharp estimates comparing asymptotic Riemannian or sub-Riemannian metrics in 2-step nilpotent Lie groups. For each metric, we construct a Carnot metric whose square remai…
Metric Lie Groups. Carnot-Carathéodory spaces from the homogeneous viewpoint
Enrico Le Donne
This book explores geometries defined by left-invariant distance functions on Lie groups, with a particular focus on nilpotent groups and Carnot groups equipped with geodesic dista…
Notions of null sets in infinite-dimensional Carnot groups
Nathaniel Eldredge, Maria Gordina, Enrico Le Donne +1
We study several notions of null sets on infinite-dimensional Carnot groups. We prove that a set is Aronszajn null if and only if it is null with respect to measures that are convo…
Escape from compact sets of normal curves in Carnot groups
Enrico Le Donne, Nicola Paddeu
In the setting of subFinsler Carnot groups, we consider curves that satisfy the normal equation coming from the Pontryagin Maximum Principle. We show that, unless it is constant, e…
Carnot rectifiability and Alberti representations
Gioacchino Antonelli, Enrico Le Donne, Andrea Merlo
A metric measure space is said to be Carnot-rectifiable if it can be covered up to a null set by countably many biLipschitz images of compact sets of a fixed Carnot group. In this…
Rough similarity of left-invariant Riemannian metrics on some Lie groups
Enrico Le Donne, Gabriel Pallier, Xiangdong Xie
We consider Lie groups that are either Heintze groups or Sol-type groups, which generalize the three-dimensional Lie group SOL. We prove that all left-invariant Riemannian metrics…